Events
DMS Colloquium: Dr. Justin Lyle |
| Time: Jan 31, 2025 (01:00 PM) |
| Location: 352 Parker Hall |
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Details: (Refreshments will be served in Parker 144 after the talk)
Speaker: Dr. Justin Lyle (Auburn University) Title: Homological Aspects of Commutative Rings
Abstract: Homological methods have been integral to our understanding of both commutative and noncommutative algebras since the so-called "Homological Invasion" of the 1950's and have led to solutions of numerous problems not intrinsically homological in nature. Despite this, there are several fundamental aspects that remain mysterious, with several problems from the 1950s-1970s remaining stubbornly open, including the Finitistic Dimension Conjecture, the Nakayama Conjecture and its generalized variant, the Tachikawa Conjectures, and the Auslander-Reiten Conjecture. In this talk, we give an overview of the historical and broader contexts of these problems and discuss recent progress of the speaker on some related questions, as a consequence leading to new broad cases of the Auslander-Reiten conjecture. |